Transfer Path Analysis Method Research Articles

Damping Optimization Method of Combine Harvester Frame Undergoing Multi-Source Excitation

The complex mechanical system of a rice combine harvester not only has various excitation sources, but also, the vibration transmission path between each working device and the vibration contribution characteristics to the frame are not clear, so it is difficult to perform a reduction vibration design for the sharp vibration of the rice combine harvester frame. Therefore, based on the comparison and improvement of multiple classical transfer path analysis methods, this paper analyzed the vibration transfer characteristics and transfer characteristics of each harvester by the discrete time matrix method and operating path method. In the Experimental section, through the vibration characteristic experiment firstly, this paper obtained the power spectrum variation and the most needed optimized path in the transmission path of each device under each operating condition. Secondly, through frame simulation analysis under the exciting force, we obtained the vibration damping areas that needs to be optimized. Finally, the damping optimization experiment connected with the vibration characteristic experiment, and the excitation force simulation analysis was performed. The results of the damping optimization experiment displayed that the maximum change value of the vibration acceleration of the cutting table decreased from 7.862 m·s−2 to 3.522 m·s−2, decreasing by 55.2%, and the peak amplitude of the multipoint test in the cab was 5.4, 5.3, 1.7 and 2.0 μm, respectively, which was significantly reduced, so the optimization effect was significant. This study provides theoretical support for the vibration reduction optimization of a rice combine harvester frame.

Research on decoupled transfer path analysis method and its application in hybrid mechanical systems

As a key technique of vibration control, transfer path analysis (TPA) provides theoretical support for diagnosis, analysis, evaluation, and optimization of vibration in mechanical systems. The coupling phenomena often exists in the vibration transfer paths of complex mechanical systems, which makes most of the existing TPA methods unable to accurately analyze the transfer function of the coupled paths. The classical transfer path analysis (CTPA) is an effective method to solve the problem of path coupling, but it changes the inherent characteristics of the system, the results can not accurately reflect the vibration transfer characteristics of the system. In order to overcome the disadvantages of CTPA method, a decoupled transfer path analysis (DTPA) method is proposed in this paper, and the implementation process of this method is introduced by taking a hybrid mechanical system as an example. The results show that DTPA method can solve the path crosstalk problem and accurately calculate the transfer function of each path.

Operational transfer path analysis based on neural network

Noise, vibration, and harshness (NVH) issues induced by vibrating source to receivers are sensitive concerns in the automotive industry, significantly determining the product quality. Transfer path analysis (TPA) serves as a crucial tool in addressing these concerns. However, classical and component-based TPA methods necessitate the measurement of all transfer functions associated with the NVH phenomenon, causing high experimental costs; moreover, operational TPA (OTPA) involves matrix inversion processes that may result in the loss of important information. In this study, a neural network-based OTPA (NOTPA) method is proposed that eliminates the need for a matrix inversion process and utilizes only operational measurement. To derive the physical meaning of transmissibility obtained from the trained neural network model, the learning algorithm for NOTPA was developed, and appropriate learning rules were applied to the model. In the general neural network model, training was performed using real-valued parameters. However, the phase of the signal is crucial information in the theoretical formulation of TPA; thus, a complex-valued propagation algorithm was established. Furthermore, an appropriate activation function was chosen to derive the actual transfer mechanism from the trained complex-valued parameters. To experimentally verify the NOTPA method, a testbed resembling automotive vehicle structure was constructed. Estimation of sound pressure and noise contribution analysis were conducted using the NOTPA method and compared with conventional TPA methods. The proposed method demonstrated higher accuracy compared to the conventional OTPA method and successfully identified the main transfer path compared to the classical TPA. Furthermore, by comparing the estimated sound pressure according to the architecture of the model, the consistency of the proposed model was verified.

An Examination of Component-Based TPA Performance and Feasibility for Steering Motors

The swift progression in the automotive sector has spurred the demand for electric power-assisted steering systems, heralding a transformation towards a more effortless, fluid, and pleasurable driving experience. However, the inherent generation of substantial noise levels within the vehicle’s cabin during the operation of these systems, can compromise the comfort of occupants, underscoring the criticality of acoustics analysis in the advancement of auxiliary systems. As long-established tools for Noise, Vibration, and Harshness (NVH) diagnostics, Transfer Path Analysis (TPA) techniques are central to studying noise propagation within vehicles. Component-based TPA, with its strength in identifying interface forces in mechanical structures, has gained a foothold in the industry due to its numerous advantages. We aim to shed light on the individual acoustic properties of the electric motor, thereby gaining a more nuanced understanding of the system’s behavior. We first lay out a brief theoretical background on relevant TPA methods, followed by the presentation of our findings from experimental studies. This paper continues our commitment to advancing the precision and practical use of TPA methodologies in automotive system analysis.

Noise contribution analysis of road noise with transfer path analysis based on neural network in the box car system

This paper introduces a new approach for transfer path analysis (TPA) combined with neural network technique. For the TPA experiment, the box car model consisting of active and passive systems were manufactured, and road noise simulation experiment were conducted through shaker excitation at various locations. Time domain data was measured and converted into a large amount of complex-valued frequency domain data according to the acquisition block for training the neural network model. The number of layers and nodes of the model were determined by considering the physical characteristics of the system, and normalization and momentum were adjusted to improve accuracy and calculation efficiency. The reliability of the model was verified by comparing the noise contribution results with the classical TPA method. Unlike the existing TPA methods, only the operating data is needed to perform the neural network based TPA. This proposed method reduces the cost of measurement step such as impact test to identify the propagation paths of the noise.

Input force contribution separation method for utilizing blocked force and operational TPA

In recent years, various transfer path analysis (TPA) methods have been proposed to separate contribution from multiple input points to the response point. In general, TPA methods require transfer function from input to the response points by hammering tests. However, obtaining accurate contribution becomes difficult in case the transfer function varies according to the operating condition or the complexity of the transfer path. In this study, we then considered input force contribution separation method for the difficult condition by combining operational TPA and blocked force used in component TPA. In the method, blocked force in the operational condition is obtained by component TPA at first, and operational TPA is applied between the obtained blocked force and the response point acceleration signals to obtain the transfer function without hammering tests. The contribution is calculated by multiplying the blocked force and the transfer function at the condition. As the verification, the proposed method was applied to a simple vehicle model equipped with a motor. And the response point vibration could be decreased well by measuring the high contributing part according to the contribution separation result. Through the verification test, the effectiveness of the proposed procedure was confirmed.

Estimation of Impact Loads Transmitted to Vibro-Ripper Housing Using Transfer Path Analysis

This study aimed to estimate impact loads delivered to vibro-ripper housing through link modules, together with loads transmitted in various directions. Housing vibration resulting from impact loads generated during the operating condition and frequency response functions were assessed by vibration and modal experiments, respectively. Vibration data and transfer functions were applied in a transfer path analysis (TPA) model to analyze the quantified impact loads transmitted through the key components of the vibro-ripper to its housing. Impact loads derived by TPA for different housing parts were compared with those in the tooth derived from load-cell measurements, validating the TPA method. As a result of the verification, the impact load calculated by the TPA method was 193.7 kN, whereas that from the striking force measured by the load cell was 220 kN, a difference of 12.3%. The results of this study may be important input values for numerical analysis in equipment design and can be used as key data for structural safety evaluation and optimization. In summary, this paper introduces the vibration-based TPA method and considers its applicability to construction machinery exposed to impact vibration and loads.

Research on fast optimal reference sensor placement in active road noise control

The noise reduction performance of the active road noise control (ARNC) system highly depends on the location of the reference sensors. Generally, the optimal sensor locations are evaluated by calculating the multiple coherence function (MCF) between all possible reference signal combinations with road noise. However, this trial-and- error method becomes time-consuming when the number of candidate locations is large. The transfer path analysis method can select the optimal sensor locations quickly while with low accuracy. Therefore, this article proposes two fast optimal sensor placement (FOSP) methods, namely, Wiener filter (WF)-FOSPand the MCF-FOSP, respectively. In both methods, the sensors are iteratively extended to the desired number, and each added sensor maximizes the predicted noise reduction of this iteration loop. Numerous ARNC simulations based on measured signals are conducted to illustrate the performance of the proposed two methods in terms of efficiency and accuracy. The results demonstrate that the WF-FOSP method provides the best comprehensive performance. The data analysis for one operating condition takes three minutes, and the absolute error is within 5% with respect to the benchmark. In addition, two schemes are discussed to obtain a set of sensor locations compatible with the noise reduction requirement of different operating conditions. The sensor locations can achieve a maximum average noise reduction of 7.29 dB(A) under four operating conditions.

Turbo generator vibration source identification based on operational transfer path analysis technology

Unstable vibrations in rotating machinery can stem from various causes, making it challenging to determine their origins. This research introduces the operational transfer path analysis method (OTPA) as a means to identify the causes of turbo generator vibrations. The model takes operational parameters, such as power and current, as input, and the vibration amplitude as output, to establish the source analysis model. To address the ill-conditioned input matrix, the singular value decomposition method is employed. By solving the transmissibility matrix and analyzing parameter contributions, the primary factors influencing vibration are identified. This method is applied to analyze the vibration sources in a 660 MW turbine generator unit. The generator experienced unstable vibration of unknown origin for a certain period. Operational transfer path analysis revealed that hydrogen pressure, hydrogen temperature, and bearing temperature significantly impacted the vibrations. Thermal imbalances and shaft misalignment in the generator rotor were inferred as the likely causes. Through adjustments to hydrogen pressure and temperature, the generator vibration was controlled until the next overhaul. Subsequent maintenance revealed partial blockage of the hydrogen ventilation holes, leading to rotor thermal imbalances. The feasibility of this method was confirmed. The objective of this study is to present an effective data-driven model for identifying the main influential parameters among numerous variables. This model can be applied to intelligent fault diagnosis in power generation units.

Development of a novel hybrid method to evaluate driving comfort in an all-terrain vehicle using transfer path analysis and transfer function analysis

Vehicle comfort has become a buzzword in the automobile sector and continuous research is going on in this domain. Every automobile manufacturer would like to take the lead in vehicle comfort so as to attract more customers. Noise, vibration and harshness (NVH) testing is very important for improving the driving comfort of a vehicle. Driving comfort is directly related to the driving ability and health of the driver. Many international organisations have laid down guidelines for measuring driving comfort and categorise it in a range from comfortable to extremely uncomfortable. The present study adopts an experimental approach to determine the driving comfort in all-terrain vehicles (ATVs) by measuring frequency-weighted root-mean-square (RMS) accelerations at all the driver contact points in three mutually perpendicular directions as per the guidelines laid down in ISO 2631-1:1997 and ISO 5349-1:2001. The low-amplitude high-frequency engine vibrations are attenuated by performing transfer path analysis (TPA) of the vehicle roll cage before and after design modifications. The performance of the engine isolator mount is evaluated by carrying out transfer function analysis (TFA) of the active and passive engine mount vibrations. A novel hybrid approach comprising the TPA and TFA methods is used to attenuate the engine vibrations. The test result shows the effectiveness of the design modifications at the footrest, whereas there is moderate to low effectiveness at the steering and seat, respectively.

Structural energy transfer to the jacket foundation of an offshore wind-wave coupling device based on absolute transmissibility function

During the long-term operation of an offshore fixed wind-wave coupling device, the structure is subjected to excitation due to the operation of the wave energy device, harmonic excitation due to the impeller rotation, and environmental excitation. In this study, the whale optimization algorithm (WOA) modified by a random mutation strategy was used to optimize the variational mode decomposition (VMD) parameters and eliminate the effect of environmental noise. Then, the normalization transfer path analysis (N-TPA) method based on the absolute transmissibility function (ATF) was used to analyze the transfer path from each vibration source to the target point. The energy transfer among the structures of the wind-wave coupling device was studied; accordingly, the contribution of the subsystems was intuitively displayed to determine the pile with the highest energy when subjected to external loads. Compared to the traditional transfer path analysis (TPA) method based on the transmissibility function (TF), the method developed in this study can overcome the ocean noise problem through the improved WOA-VMD method and yield more accurate transfer path analysis results. To verify the effectiveness of the method developed in this study, numerical research, simulation, and physical model experiments were conducted using the 5-DOF system theoretical model, finite element model, and physical model. The contributions of the subsystems to the operational state of the structure were analyzed. The results demonstrated that the proposed method could be used to evaluate the stability of each structural element such that appropriate measures can be taken. This provides a reference for the development and stable operation of fixed wind-wave coupling devices.

Effective acceleration design for solving excessive vibration in the cockpit

To address the issue of vibration discomfort caused by excessive vibration in the cockpit, a method that allocates vibration reduction index (VRI) to different vibration transfer paths is proposed. By combining the identified vibration contribution of vibration sources using the transfer path analysis (TPA) method with the evaluated relative difficulty levels of vibration reduction design in these paths through the fuzzy analytical hierarchy process, the allocation weights can be constructed, which enables the VRI at the target location can be allocated to these paths, and effective amplitude values of acceleration transferred by these paths can be designed. Then, the specific process of the method is illustrated by a study case on the acceleration designed at the cockpit floor-seat connection. The results show that to achieve a vibration discomfort level that cannot be felt at this location, the effective acceleration amplitudes transferred from the main landing gear compartments and the engines need to be reduced by at least 61.55 % and 77.23 %, respectively. This method can effectively allocate acceleration transferred and guide the cockpit vibration comfort design.

Experimental study of component-based transfer path analysis hybrid methods applied to a helicopter

The noise prevailing inside the helicopter’s cabin always presents a problem for the operators of this vehicle. It is a source of annoyance and represents a pressing problem in the helicopter industry, causing manufacturers to constantly seek new technologies and solutions to reduce noise. This article aims to present a component-based transfer path analysis method (CB-TPA) and its application to the prediction of structure-borne noise transmitted into the cabin of a helicopter due to its main gearbox. The approach characterizes the source using a laboratory test bench and uses various CB-TPA methods to couple the blocked force to the dynamics of the receiving structure. The article details the used methods, their main assumptions, the experimental test configurations, and discusses the results compared to the classical in situ CB-TPA method. The effects of important parameters such as the completeness of the input and transfer mobility matrices are also discussed. It is shown that the presented methodology can correctly and accurately capture the noise in the cabin from a decoupled characterization of the source and the receiving structure.

Fault tracing of gear systems: An in-situ measurement-based transfer path analysis method

A transfer path analysis method based on the in-situ measurement is proposed for the fault tracing of parallel axis gear systems. A virtual decoupling technique is used to achieve the in-situ measurement of the decoupled frequency response function (FRF) between bearing positions and measuring points on housing, avoiding the tedious test procedure and non-representative assembly conditions caused by the physical decoupling. Based on the decoupled FRF and the responses of the gearbox housing, the bearing force is identified using the Tikhonov regularization theory. Then the frequency-dependent path contribution, which will be used to perform the transfer path analysis, is obtained by multiplying the decoupled FRF and the bearing force. Finally, the fault-specific path rank order is determined using the path contribution within the resonant frequency band. This band is located by the spectral kurtosis algorithm. Based on the proposed in-situ path analysis, fault tracing is conducted by determining the dominant transfer path. The effectiveness of the proposed path analysis method is verified both numerically and experimentally. A two-stage parallel axis gear test rig with localized defects is utilized to demonstrate the efficacy of the proposed fault tracing strategy. Moreover, based on the path analysis, a physically-interpretable signal decomposition method is proposed to enhance the fault feature. Through this decomposition method, the fault indicator of the weakest fault type (chipped tooth) can be magnified by 204%. The proposed transfer path analysis method provides a feasible strategy for fault tracing, feature enhancement and incipient fault diagnosis of parallel axis gear systems.

Comparison of transfer path characteristics for different wind turbine drivetrain variations

To reduce acoustic emissions of a wind turbine (WT), the source of the vibrations (e.g. blades, gearbox), the emitting surfaces (e.g. blades, tower, nacelle cover) and the transmission between the source and surface have to be studied. The focus of this paper lies on a method to identify relevant transfer paths between the WT drivetrain and the sound-emitting surfaces and their respective contribution. The identified transfer paths can be used to improve turbine acoustics, especially by identifying problematic transmission areas.This paper will cover the application of transfer path analysis methods for different wind turbine drivetrains. The method will be applied to an MBS model of a 3 MW turbine. Different Bearing arrangements of the drivetrain and their influence on the Transfer path are compared. With the result of the TPA, developers will be able to determine critical contributions to the tonal behavior of the turbine and optimize either the transfer characteristics or the excitation specifically responsible for tonal behavior. The methods described can be applied to field measurement as well as an MBS-Model of the turbine to be able to optimize transfer characteristics during development.

Numerical and experimental analysis on helicopter's main rotor transmission for predicting structure-borne noise (SBN) using CB-TPA methods

A large number of a vehicle's mechanical systems are responsible for tonal vibrations, which propagate through the connected structures to radiate structure-borne noise into the cabin. In the literature, transfer path analysis (TPA) methods make it possible to solve vibro-acoustic problems using sub-structuring applications. This paper presents a case study of a heavy-active component connected to a plate backed cavity, using Component-Based transfer path analysis methods. The studied academic system is representative of a helicopter's main transmission. Both numerical and the experimental characterization are used to discuss the effect of several parameters, such as coupling (in-situ) vs decoupling (sub-structuring), completeness of the used transfer function matrix, the accuracy of the inversion method, as well as the rigidity of the test bench used to identify the equivalent forces. It is shown both numerically and experimentally that by using part of the frequency response functions matrix, one can reconstruct the response of both vibration and acoustic targets locations, even by decoupling the system and characterizing the equivalent forces on a test bench.

Numerical investigation of the effects of model and operator uncertainties on component-based transfer path analysis methods with substructuring applied to aircraft-like components

Hydraulic pumps are considered to have a major contribution to the structure borne noise generated inside aircrafts. Methods such as Component-Based Transfer Path Analysis (CB-TPA) are promising tools for aircraft manufacturers to build internal processes for the specification, design and validation of the impact of vibrating systems on new aircrafts. However, the experimental applicability of these methods remains limited due to some experimental difficulties. CB-TPA' formulation is based on dynamical quantities, which require the determination of terms related to rotational degrees of freedom. Virtual Point (VP) or Equivalent Multi-Point Connection (EMPC) methods are commonly employed for this purpose, but both result in more cumbersome experimental set-ups and increased measurement uncertainties. The implementation of these methods is difficult in the case of a flat and thin receiving structure as commonly encountered in aircraft applications, since in-plane translational excitations have to be applied and the access to the vibrating system/structure interface points is limited. In this work, a decoupling procedure is used to overcome these issues. A numerical model is used to investigate the influence of model and operator uncertainties on the CB-TPA' predictions, when the dynamical quantities are provided by VP and EMPC methods including the decoupling procedure.

Application of the transfer path analysis to vehicle doors

Transfer path analysis (TPA) is a proven method for identifying critical structure-borne and airborne sound paths. The basic idea is to divide the overall system into an exciting active component (source) and a passive component, e.g. the mechanical structure to be investigated, with their respective measurement points. By separating them, two independent systems are created, whereby on one hand, the excitation behaviour can be characterised and on the other hand, the transmission behaviour can be assessed. Finally, both systems are validated by comparing them to each other and deciding whether changes to source or structure are required or not. The advantage is the simple description of the source as a black box without complex modelling. In this contribution, this systematic is applied to window regulator systems as they are found in vehicles. The focus is on a hybrid approach between experimental and numerical transfer path analysis. For this purpose, the basic workflow of suitable TPA methods is discussed. This includes the operational measurement of different exciting electric motors variants, the determination of the transfer functions of the structure, the calculation of the contact forces and the analysis of the individual transfer paths.

Analysis and Experimental Study of Excitation Force Transfer Path of Optical Satellite Refrigeration Module

When the problem of the reaction force under the receiver structure is complicated, the existing force-based transfer path analysis method is not suitable for its analysis. Therefore, an improved reaction force transfer path analysis method is proposed in this paper. In the transfer path analysis method based on the modal superposition method, the penalty function method is introduced, and the path contribution of the receiving end reaction force is evaluated by analyzing the displacement response of the connection between the transfer path and the receiving end. A simulation analysis of a satellite refrigeration module vibration isolation device designed by the research group identified the main factors affecting the vibration isolation efficiency of the vibration isolation ring, and provided guidance for subsequent further optimization. The device was tested and analyzed by building an experimental platform, and the obtained simulation data fit well with the test data. These conclusions further show that the proposed analysis method can more accurately and conveniently analyze the path contribution of the receiving end reaction force under specific working conditions. This method is suitable for analyzing the transfer path of the reaction force at the receiving end in the design stage.

Effects of mobility matrices completeness on component-based transfer path analysis methods with and without substructuring applied to aircraft-like components

Structure borne noise induced by vibrating systems is considered as a major contribution to the noise generated inside vehicles and can be assessed using Transfer Path Analysis (TPA) methods. Their theoretical formulation requires the mobility of either the vibrating system, the receiving structure or the assembly of the two components according to all Degrees of Freedom (DoFs). However, rotational and in-plane DoFs cannot be measured easily and their determination may result in a more complex experimental set-up or an increase in measurement uncertainties. The need for assessing the full mobility matrices thus deserves to be investigated. In this work, the robustness of multiple TPA methods dedicated to the design and validation phases of aircraft light equipment is investigated numerically according to the mobility matrices completeness and by considering several configurations of assemblies (i.e., different active source properties, different numbers of contact points). Numerical models have been developed to simulate a source with controlled vibratory behavior and the spatial averaged mean-square velocity on the receiving structure is used as an objective indicator of the method’s robustness. For proper predictions accuracy, it is shown that the required completeness should account for the terms of highest amplitude and thus depends on the (i) TPA method, (ii) active behavior of the source and (iii) coupling configuration. A completeness involving all the DoFs is generally required for TPA methods based entirely on the mobility of the decoupled components. Otherwise, the omission of rotational or in-plan DoFs could be suitable for TPA methods based on the mobility of the assembly.